ATD: Algorithms for Point Processes on Networks for Threat Detection

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We live in a world full of networks: contact and social networks connect us to our family, friends and colleagues; computer networks such as Internet allow us to access huge amount of data and information remotely; traffic and logistical networks deliver people, water/food, and all kinds of goods faster than ever before. While we enjoy the conveniences brought by these networks, we must also be aware of the threats and harms if they get jeopardized by, for example, infectious virus, cyber-attacks, etc. The goal of this project is to develop computational algorithms for automated early threat detection based on novel and rigorous mathematical modeling and data analysis concepts. In particular, the activities generated by human and other sources on these networks are modeled as the so-called interactive stochastic point processes. These dynamics are studied and inferred in a mathematical framework of jump stochastic differential equations, which is further extended to integrate mean-field approximation and deep learning techniques that fully leverage the existing big data for fast and accurate threat detection. This project will exploit three closely related computational problems in-depth: influence prediction, optimal sensor allocation, and source identification, all of which are fundamental in threat detection applications on large, heterogeneous, real-world networks.This project will exploit two novel approaches to influence prediction based on a jump stochastic differential equation (JSDE) formulation and an integration of mean field approximation and deep learning techniques. The JSDE formulation yields a concise and exact mathematical formulation of the temporal point process that takes into account the known network structure and mechanism of epidemic spread; and the deep neural mean field approach deduced from JSDE formulation maps the classical difference method in numerical analysis into a structured multi-layer residual network, where the unknown bias of mean field approximation can be effectively learned from observed cascade data for rapid influence prediction. These prediction algorithms will be used in the optimal sensor allocation and epidemic source identification problems for threat detection and mitigation. The results produced in this project are expected to make significant contributions to our understanding of interdependent activities on large-scale heterogeneous networks and the development of new, efficient algorithms for threat detection. The outcomes of the project include novel computational techniques, rigorous mathematical theory and analysis, and efficient numerical algorithms for threat detection applications.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.